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09/01/2023
Bichromatic Perfect Matchings with Crossings
We consider bichromatic point sets with n red and n blue points and stud...
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05/16/2023
Using SAT to study plane Hamiltonian substructures in simple drawings
In 1988 Rafla conjectured that every simple drawing of a complete graph ...
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03/24/2023
Roudneff's Conjecture in Dimension 4
J.-P. Roudneff conjectured in 1991 that every arrangement of n ≥ 2d+1≥ 5...
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03/07/2023
An extension theorem for signotopes
In 1926, Levi showed that, for every pseudoline arrangement 𝒜 and two po...
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10/21/2022
Blocking Delaunay Triangulations from the Exterior
Given two distinct point sets P and Q in the plane, we say that Q blocks...
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08/25/2022
Arrangements of Pseudocircles: On Digons and Triangles
In this article, we study the cell-structure of simple arrangements of p...
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05/17/2022
Coloring circle arrangements: New 4-chromatic planar graphs
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement gr...
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03/14/2022
Erdős–Szekeres-type problems in the real projective plane
We consider point sets in the real projective plane ℝP^2 and explore var...
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11/24/2021
Tight bounds on the expected number of holes in random point sets
For integers d ≥ 2 and k ≥ d+1, a k-hole in a set S of points in general...
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09/22/2021
On Crossing-Families in Planar Point Sets
A k-crossing family in a point set S in general position is a set of k s...
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05/18/2021
A SAT attack on higher dimensional Erdős–Szekeres numbers
A famous result by Erdős and Szekeres (1935) asserts that, for every k,d...
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07/30/2020
Many Order Types on Integer Grids of Polynomial Size
Two point configurations {p_1,…,p_n} and {q_1,…,q_n} are of the same ord...
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05/26/2020
Topological Drawings meet Classical Theorems from Convex Geometry
In this article we discuss classical theorems from Convex Geometry in th...
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03/02/2020
Holes and islands in random point sets
For d ∈ℕ, let S be a finite set of points in ℝ^d in general position. A ...
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11/06/2019
On the Average Complexity of the k-Level
Let A be an arrangement of n lines in the Euclidean plane. The <i>k-leve...
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08/14/2019
Minimal Representations of Order Types by Geometric Graphs
In order to have a compact visualization of the order type of a given po...
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11/15/2018
A Note On Universal Point Sets for Planar Graphs
We investigate which planar point sets allow simultaneous straight-line ...
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10/23/2018
On orthogonal symmetric chain decompositions
The n-cube is the poset obtained by ordering all subsets of {1,...,n} by...
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07/29/2018
On L-shaped Point Set Embeddings of Trees: First Non-embeddable Examples
An L-shaped embedding of a tree in a point set is a planar drawing of th...
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07/27/2018
On Disjoint Holes in Point Sets
A k-hole in a point set S ⊆R^2 is a subset X ⊆ S, |X|=k, such that all p...
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12/06/2017
Arrangements of Pseudocircles: On Circularizability
An arrangement of pseudocircles is a collection of simple closed curves ...
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08/21/2017